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Where are the Book of Mormon plates now?

 

 (Replica of The Book of Mormon plates.)  

The Prophet Joseph Smith records that Moroni was in "charge" of the Book of Mormon plates.  In other words Moroni was the caretaker of the plates.  
When Joseph Smith received the plates, he was told that when he had finished translating the plates “arrangements” would be made to deliver them back to Moroni.

“…by the wisdom of God, they remained safe in my hands, until I had accomplished by them what was required at my hand. When  according to arrangements, the messenger called for them, I delivered them, [the Book of Mormon plates] up to him; and he has them in his charge until this day, being the second day of May, one thousand eight hundred and thirty-eight."    (Joseph Smith History 1:60)
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Evidence indicates that the Book of Mormon plates were then put in a depository cave which was filled with many other "sacred engravings”.

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Discourse by Elder Orson Pratt, 1877.

“…these plates now hidden in the hill Coumorah…”  
(Discourse by Elder Orson Pratt 1877 Journal. of Discourses. Vol. 19, p. 218)

 

 

 

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  Discourse by Brigham Young June 17, 1877.
"Oliver Cowdery went with the Prophet Joseph when he deposited these plates. Joseph did not translate all of the plates; there was a portion of them sealed, which you can learn from the Book of Doctrine and Covenants.  When Joseph [Smith] got the plates, the angel instructed him to carry them back to the hill Cumorah, which he did.  Oliver, [Cowdery], says that when Joseph and Oliver went there, the hill opened, and they walked into the cave, in which there was a large and spacious room."

"He says he did not think, at the time, whether they had the light of the sun or artificial light; but that it was just as light as day. They laid the plates on a table; it was a large table that stood in the room. Under this table there was a pile of plates as much as two feet high, and there were altogether in this room more plates than probably many wagon loads; they were piled up in the corners and along the walls. The first time they went there the sword of Laban hung upon the wall; but when they went again it had been taken down and laid upon the table across the gold plates; it was unsheathed, and on it was written these words: “This sword will never be sheathed again until the kingdoms of this world become the kingdom of our God and his Christ.” I tell you this as coming not only from Oliver Cowdery, but others who were familiar with it, and who understood it just as well as we understand coming to this meeting, enjoying the day, and by and by we separate and go away, forgetting most of what is said, but remembering some things. So is it with other circumstances in life. I relate this to you, and I want you to understand it. I take this liberty of referring to those things so that they will not be forgotten and lost. Carlos Smith was a young man of as much veracity as any young man we had, and he was a witness to these things. Samuel Smith saw some things, Hyrum saw a good many things, but Joseph was the leader."

 Journal of Discourses Vol.19, Page 38

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Heber C. Kimball in 1856 recorded that the Book of Mormon plates were returned into a depository "cave" or room.  
This depository "cave" or room and the event of seeing and being inside this cave, according to Heber C. Kimball, was a "vision".
“…the vision that Joseph [Smith] and others had, when [they went] into a cave in the hill Cumorah..."  (Journal of Discourses Vol. 4, Page 105)

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  << David Whitmer

 

A Dr. Poulson, living in Ogden, wrote to the editors of the Deseret News concerning a visit he had had with David Whitmer. The News published portions of the letter, part of it is as follows.  

 

Dr. Poulson - Where are the plates now?

David Whitmer—In a cave, where the angel has hidden them up till the time arrives when the plates, which are sealed, shall be translated. God will yet raise up a mighty one, who shall do his work till it is finished and Jesus comes again.

Dr. Poulson - Where is that cave?

David Whitmer— In the state of New York.

Dr. Poulson - In the Hill Cumorah?

David Whitmer— No, but not far from that place. 

(Deseret News, August 16, 1878.)

 

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Evidence indicates that there are two different hills, each hill is called Cumorah.
The hill Cumorah located in the State of New York.
The hill Cumorah in the Book of Mormon located in Mesoamerica.
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Conclusion:
With the various statements and available evidence, it is not evident which Hill Cumorah, the plates are deposited in.  
-- Are they in the Hill Cumorah, the exact hill that the plates were despsited in the stone box, located in the State of New York?
--  Or, another Hill Cumorah close by in New York?  
--  Or, are they deposited in the Hill Cumorah located in Mesoamerica as talked about in the Book of Mormon?

Regardless of the location, all of these plates are "deposited unto the Lord" and will be brought forth in his own do time.  (Mormon 1:3 & Mormon 2:17)
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Additional Information: 
The Hill Cumorah
A Vision of a Depository Cave in a hill called Cumorah